An action \left( \gamma ,\alpha \right) of a locally compact group G on a Hilbert pro-C^{\ast }-bimodule \left( X,A\right) induces an action \gamma \times \alpha of G on A\times _{X}\mathbb{Z} the crossed product of A by X. We show that if \left( \gamma ,\alpha \right) is an inverse limit action, then the crossed product of A\times _{\alpha }G by X\times_{\gamma }G respectively of A\times _{\alpha ,r}G by X\times_{\gamma ,r}G is isomorphic to the full crossed product of A\times _{X}\mathbb{Z} by \gamma \times \alpha respectively the reduced crossed product of A\times _{X}\mathbb{Z} by \gamma \times \alpha.

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Author(s)

Joiţa, Maria, Munteanu, Radu B.